Effect of hydration shell on the energy of nanobubbles in water

It is shown that the energy of a charged nanobubble (CNB) is formed by the partial energies of free and bound charges in vacuum, as well as by the polarization energies of the dielectric in the hydrate layer and beyond it. The hydrate layer increases the CNB energy by 5.3 times at a radius of 5 nm and by no more than 8% at a radius of more than 25 nm, by a value close to the energy of this layer. The polarization energy of the dielectric medium is almost 2 orders of magnitude greater than the energy of charges in vacuum in the hydrate and diffuse layers. At a radius of less than 26 nm, the total electrostatic energy of the CNB inside the hydrate shell is greater than outside it. In larger nanobubbles, more energy is concentrated outside the hydrate shell.